Abstract: Multi-channel SAR in azimuth, which can be used to suppress the Doppler ambiguity to get the High-Resolution Wide-Swath (HRWS) SAR images, suffers from the amplitude and phase mismatch among the channels. Based on the analysis of the characteristics of the multi-channel SAR that the energy of radar echoes outside the Doppler bandwidth is much lower than that in the Doppler bandwidth, this paper presents a novel data-based phase error estimation method for HRWS SAR system. With the assumption that the echoes outside the Doppler bandwidth are approximately zero, the estimation of phase biases in the multi-channel HRWS SAR system can be translated into the Constant Module Quadratic Programming (CMQP) issue. The phase bias among the channels can be extracted using the solutions of the classical CMQP optimization methods, such as Eigen-Value Relaxation (EVR), Semi-Definite Relaxation (SDR) and so on. The theoretical analysis reveals that the presented method can be viewed as an adaptive weighted least square estimation of the phase biases among the channels. The performance of presented method is validated with the experiments of simulated multi-channel SAR data.